Theorem 3ad2antl1 1186

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antl1	|- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Proof of Theorem 3ad2antl1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ch ) -> th )
3	2	3adantl2 1181	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1007

This theorem is referenced by:  acexmid  6027  f1oen4g  6968  f1dom4g  6969  ordiso2  7294  addlocpr  7816  distrlem1prl  7862  distrlem1pru  7863  ltsopr  7876  addcanprlemu  7895  fzo1fzo0n0  10485  pfxsuffeqwrdeq  11345  prodfap0  12186  prodfrecap  12187  muldvds2  12458  dvds2add  12466  dvds2sub  12467  dvdstr  12469  qusaddvallemg  13496  mulgnnsubcl  13801  mulgpropdg  13831  ringidss  14123  lmodprop2d  14444  cnpnei  15030  upxp  15083  lgsval4lem  15830  clwwlkccatlem  16341  clwwlkccat  16342